Question about these thermal expansion coefficient units (m/mK)

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Discussion Overview

The discussion revolves around the units of thermal expansion coefficients, specifically the notation of 10^-6 m/mK. Participants explore the meaning and implications of these units in the context of linear thermal expansion.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses confusion about the unit 10^-6 m/mK, questioning if it represents micrometers divided by milliKelvins.
  • Another participant clarifies that the unit represents an absolute thermal expansion for a fixed length, not as a proportion of length.
  • A different viewpoint suggests that the unit can be understood as meters divided by (meters times Kelvin), emphasizing that it simplifies to a ratio of expansion per degree Kelvin in one dimension.
  • A participant questions the necessity of including the units if they can be canceled out mathematically.
  • Another response indicates that while the units can be canceled for mathematical purposes, they provide important contextual information about the nature of the measurement, specifically relating to microns per meter for each degree Kelvin.
  • There is a mention of the usefulness of dimensional analysis in validating answers, particularly in unfamiliar contexts.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and interpretation of the units, indicating that there is no consensus on the importance of the unit notation in conveying information about thermal expansion.

Contextual Notes

Some assumptions about dimensional analysis and its teaching may not be universally applicable, and the discussion does not resolve the question of the necessity of the unit notation.

kasnay
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so I have never seen this unit before. 10^-6m/mK for the thermal expansion (linear expansion). I believe this unit is micrometers divided by mili kelvins?
 
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So that would be an absolute thermal expansion for a fixed length, not as a proportion of length.
 
I believe it's:meters / (meter x Kelvin) (not milliKelvin)

Simplifying ('cancel' the meters), it's just a ratio of expansion per degK (in one dimension)
 
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okay thank you, well now my question is why did they bother putting it there if it could be cancelled?
 
It may be 'cancelled' for mathematical purposes. The information that it conveys helps you to make sense of what the number actually represents. In this case, 1 micron per meter of length for every 1 DegK. I don't know if they explicitly teach dimensional analysis these days, but it is a very useful way to check the validity of your answer - particularly if you're doing something unfamiliar.
 

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